If salespeople have to handle in-store pickups from online purchases, that cuts into their ability to make new sales on the floor, Connor said. Plus, clerks don't make any money when customers buy products online -- even if they helped them find the very best casserole dish.

It's not clear how Bloomingdale's would be able to track purchases store customers later made online.

"I am sure the company can work on a tracking system," Connor said. "There's technology for everything."

Bloomingdale's spokeswoman Anne Keating said the company isn't able to comment on what this kind of system would look like.

"We are trying to reach a fair and reasonable agreement that represents our associates' commitment to our customers," she told CNNMoney. "But we have to address the competitive business realities we face. And we have to be flexible about the way we take care of our customers."

The union covers 2,000 workers at the flagship location.

Connor said most are paid entirely on commission. Bloomingdale's said this is "totally wrong," and store employees receive a variety of different pay packages.

The workers' most recent agreement was signed in 2012.

The union says a strike is on the table if negotiations go south before May 1. The last time Bloomingdale's workers staged a walkout at the flagship store was in 1965.